Probabilistic Clustering and Shape Modelling of White Matter Fibre Bundles Using Regression Mixtures

We present a novel approach for probabilistic clustering of white matter fibre pathways using curve-based regression mixture modelling techniques in 3D curve space. The clustering algorithm is based on a principled method for probabilistic modelling of a set of fibre trajectories as individual sequences of points generated from a finite mixture model consisting of multivariate polynomial regression model components. Unsupervised learning is carried out using maximum likelihood principles. Specifically, conditional mixture is used together with an EM algorithm to estimate cluster membership. The result of clustering is a probabilistic assignment of fibre trajectories to each cluster and an estimate of cluster parameters. A statistical shape model is calculated for each clustered fibre bundle using fitted parameters of the probabilistic clustering. We illustrate the potential of our clustering approach on synthetic and real data.